Solve The Following: $32 \div 4 + 4 \times 8 =$ ?A) 40 B) 42 C) 32 D) 96
Introduction
In this article, we will be solving a mathematical expression that involves both division and multiplication. The expression is 32 ÷ 4 + 4 × 8, and we need to find the value of this expression. We will follow the order of operations (PEMDAS) to solve this expression.
Understanding the Order of Operations
The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next (e.g., 2^3).
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Solving the Expression
Now that we understand the order of operations, let's apply it to the expression 32 ÷ 4 + 4 × 8.
Step 1: Divide 32 by 4
The first operation in the expression is the division of 32 by 4. We will perform this operation first.
32 ÷ 4 = 8
Step 2: Multiply 4 by 8
The next operation in the expression is the multiplication of 4 by 8. We will perform this operation next.
4 × 8 = 32
Step 3: Add 8 and 32
The final operation in the expression is the addition of 8 and 32. We will perform this operation last.
8 + 32 = 40
Conclusion
Therefore, the value of the expression 32 ÷ 4 + 4 × 8 is 40.
Final Answer
The final answer is A) 40.
Discussion
This problem is a great example of how to apply the order of operations to solve a mathematical expression. It's essential to follow the order of operations to ensure that we perform the operations in the correct order.
Tips and Tricks
- Always follow the order of operations when solving mathematical expressions.
- Use parentheses to group operations and make it easier to follow the order of operations.
- Practice solving mathematical expressions to become more comfortable with the order of operations.
Related Topics
- Order of operations (PEMDAS)
- Division and multiplication
- Addition and subtraction
Further Reading
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
References
- "Mathematics for Dummies" by Mark Zegarelli
- "Algebra and Trigonometry" by Michael Sullivan
- "Mathematics: A Very Short Introduction" by Timothy Gowers
Introduction
In our previous article, we solved the mathematical expression 32 ÷ 4 + 4 × 8. In this article, we will answer some frequently asked questions related to solving mathematical expressions.
Q&A
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next (e.g., 2^3).
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: Why is it essential to follow the order of operations?
A: Following the order of operations is crucial to ensure that we perform the operations in the correct order. If we don't follow the order of operations, we may get incorrect results.
Q: What happens if we have multiple operations with the same precedence?
A: If we have multiple operations with the same precedence, we need to perform them from left to right. For example, if we have the expression 3 + 4 × 5, we need to perform the multiplication first and then the addition.
Q: Can we use parentheses to group operations?
A: Yes, we can use parentheses to group operations and make it easier to follow the order of operations. For example, if we have the expression 3 + (4 × 5), we can evaluate the expression inside the parentheses first and then perform the addition.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both operations that involve numbers, but they have different properties. Multiplication is a commutative operation, which means that the order of the numbers doesn't matter (e.g., 2 × 3 = 3 × 2). Division is a non-commutative operation, which means that the order of the numbers matters (e.g., 6 ÷ 2 ≠2 ÷ 6).
Q: Can we simplify mathematical expressions?
A: Yes, we can simplify mathematical expressions by combining like terms and eliminating any unnecessary operations. For example, if we have the expression 2 × (3 + 4), we can simplify it by evaluating the expression inside the parentheses first and then performing the multiplication.
Tips and Tricks
- Always follow the order of operations when solving mathematical expressions.
- Use parentheses to group operations and make it easier to follow the order of operations.
- Practice solving mathematical expressions to become more comfortable with the order of operations.
- Simplify mathematical expressions by combining like terms and eliminating any unnecessary operations.
Related Topics
- Order of operations (PEMDAS)
- Division and multiplication
- Addition and subtraction
- Simplifying mathematical expressions
Further Reading
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
References
- "Mathematics for Dummies" by Mark Zegarelli
- "Algebra and Trigonometry" by Michael Sullivan
- "Mathematics: A Very Short Introduction" by Timothy Gowers
Conclusion
Solving mathematical expressions can be challenging, but by following the order of operations and using parentheses to group operations, we can make it easier to solve them. Remember to practice solving mathematical expressions to become more comfortable with the order of operations.